$\dfrac{ g - 3h }{ -8 } = \dfrac{ -3g + i }{ 5 }$ Solve for $g$.
Explanation: Multiply both sides by the left denominator. $\dfrac{ g - 3h }{ -{8} } = \dfrac{ -3g + i }{ 5 }$ $-{8} \cdot \dfrac{ g - 3h }{ -{8} } = -{8} \cdot \dfrac{ -3g + i }{ 5 }$ $g - 3h = -{8} \cdot \dfrac { -3g + i }{ 5 }$ Multiply both sides by the right denominator. $g - 3h = -8 \cdot \dfrac{ -3g + i }{ {5} }$ ${5} \cdot \left( g - 3h \right) = {5} \cdot -8 \cdot \dfrac{ -3g + i }{ {5} }$ ${5} \cdot \left( g - 3h \right) = -8 \cdot \left( -3g + i \right)$ Distribute both sides ${5} \cdot \left( g - 3h \right) = -{8} \cdot \left( -3g + i \right)$ ${5}g - {15}h = {24}g - {8}i$ Combine $g$ terms on the left. ${5g} - 15h = {24g} - 8i$ $-{19g} - 15h = -8i$ Move the $h$ term to the right. $-19g - {15h} = -8i$ $-19g = -8i + {15h}$ Isolate $g$ by dividing both sides by its coefficient. $-{19}g = -8i + 15h$ $g = \dfrac{ -8i + 15h }{ -{19} }$ Swap signs so the denominator isn't negative. $g = \dfrac{ {8}i - {15}h }{ {19} }$